Question 84832
Here's a way to do these:
1) Write 0.454545... as a fraction.
Let n = 0.454545... Multiply both sides by 100.
100n =45.454545... Subtract the first equation from the second equation.

99n = 45 Finally, divide both sides by 99
n = 45/99...but n = 0.454545..., so
0.454545...= 45/99 = 5/11
{{{highlight(0.454545 = 5/11)}}}
Check this on your calculator!

2) Write 1.3666... as a fraction.

Let n = 1.3666... Multiply both sides by 10.
10n = 13.666... Multiply both sides by 10 again.
100n = 136.666... Now subtract 10n from 100n
90n = 123 Finally divide both sides by 90.
n = 123/90...but n = 1.3666... so
1.3666... = 123/90 = 41/30
{{{highlight(1.3666 = 41/30)}}}
Check this on your calculator!